IDEAS home Printed from https://ideas.repec.org/a/bpj/jossai/v8y2020i3p195-223n1.html
   My bibliography  Save this article

Implementation of Presolving and Interior-Point Algorithm for Linear & Mixed Integer Programming: SOFTWARE

Author

Listed:
  • Ndayikengurutse Adrien

    (School of Management Science and Engineering, Institute of Science and Development, Chinese Academy of Sciences, Beijing, 100190, China)

  • Huang Siming

    (Chinese Academy of Sciences, Beijing, 100190, China)

Abstract

Linear and mixed integer programming are very popular and important methods to make efficient scientific management decision. With large size of real application data, the use of linear-mixed integer programming is facing problems with more complexity; therefore, preprocessing techniques become very important. Preprocessing aims to check and delete redundant information from the problem formulation. It is a collection of techniques that reduce the size of the problem and try to strengthen the formulation. Fast and effective preprocessing techniques are very important and essential for solving linear or mixed integer programming instances. In this paper, we demonstrate a set of techniques to presolve linear and mixed integer programming problems. Experiment results showed that when preprocessing is well done, then it becomes easier for the solver; we implemented interior-point algorithm for computational experiment. However, preprocessing is not enough to reduce the size and total nonzero elements from the constraints matrix. Moreover, we also demonstrate the impact of minimum degree reordering on the speed and storage requirements of a matrix operation. All techniques mentioned above are presented in a multifunctional software to facilitate users.

Suggested Citation

  • Ndayikengurutse Adrien & Huang Siming, 2020. "Implementation of Presolving and Interior-Point Algorithm for Linear & Mixed Integer Programming: SOFTWARE," Journal of Systems Science and Information, De Gruyter, vol. 8(3), pages 195-223, June.
    • Handle: RePEc:bpj:jossai:v:8:y:2020:i:3:p:195-223:n:1
    DOI: 10.21078/JSSI-2020-195-29
    as

    Download full text from publisher

    File URL: https://doi.org/10.21078/JSSI-2020-195-29
    Download Restriction: no
    File URL: https://libkey.io/10.21078/JSSI-2020-195-29?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Robert Bixby & Edward Rothberg, 2007. "Progress in computational mixed integer programming—A look back from the other side of the tipping point," Annals of Operations Research, Springer, vol. 149(1), pages 37-41, February.
    2. Ilan Adler & Narendra Karmarkar & Mauricio G. C. Resende & Geraldo Veiga, 1989. "Data Structures and Programming Techniques for the Implementation of Karmarkar's Algorithm," INFORMS Journal on Computing, INFORMS, vol. 1(2), pages 84-106, May.
    3. Harlan Crowder & Ellis L. Johnson & Manfred Padberg, 1983. "Solving Large-Scale Zero-One Linear Programming Problems," Operations Research, INFORMS, vol. 31(5), pages 803-834, October.
    4. M. W. P. Savelsbergh, 1994. "Preprocessing and Probing Techniques for Mixed Integer Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 6(4), pages 445-454, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Patrick Gemander & Wei-Kun Chen & Dieter Weninger & Leona Gottwald & Ambros Gleixner & Alexander Martin, 2020. "Two-row and two-column mixed-integer presolve using hashing-based pairing methods," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 205-240, October.
    2. Tobias Achterberg & Robert E. Bixby & Zonghao Gu & Edward Rothberg & Dieter Weninger, 2020. "Presolve Reductions in Mixed Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 473-506, April.
    3. Wei-Kun Chen & Liang Chen & Mu-Ming Yang & Yu-Hong Dai, 2018. "Generalized coefficient strengthening cuts for mixed integer programming," Journal of Global Optimization, Springer, vol. 70(1), pages 289-306, January.
    4. Jeffery L. Kennington & Karen R. Lewis, 2004. "Generalized Networks: The Theory of Preprocessing and an Empirical Analysis," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 162-173, May.
    5. Escudero Bueno, Laureano F. & Garín Martín, María Araceli & Merino Maestre, María & Pérez Sainz de Rozas, Gloria, 2011. "A parallelizable algorithmic framework for solving large scale multi-stage stochastic mixed 0-1 problems under uncertainty," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    6. Marianna E.-Nagy & Anita Varga, 2023. "A new long-step interior point algorithm for linear programming based on the algebraic equivalent transformation," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(3), pages 691-711, September.
    7. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.
    8. Escudero, L. F. & Munoz, S., 2003. "On identifying dominant cliques," European Journal of Operational Research, Elsevier, vol. 149(1), pages 65-76, August.
    9. Feng Qiu & Shabbir Ahmed & Santanu S. Dey & Laurence A. Wolsey, 2014. "Covering Linear Programming with Violations," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 531-546, August.
    10. Alexandra M. Newman & Martin Weiss, 2013. "A Survey of Linear and Mixed-Integer Optimization Tutorials," INFORMS Transactions on Education, INFORMS, vol. 14(1), pages 26-38, September.
    11. Francisco Trespalacios & Ignacio E. Grossmann, 2015. "Algorithmic Approach for Improved Mixed-Integer Reformulations of Convex Generalized Disjunctive Programs," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 59-74, February.
    12. Codas, Andrés & Camponogara, Eduardo, 2012. "Mixed-integer linear optimization for optimal lift-gas allocation with well-separator routing," European Journal of Operational Research, Elsevier, vol. 217(1), pages 222-231.
    13. Maros, Istvan & Haroon Khaliq, Mohammad, 2002. "Advances in design and implementation of optimization software," European Journal of Operational Research, Elsevier, vol. 140(2), pages 322-337, July.
    14. Alves, Maria Joao & Climaco, Joao, 1999. "Using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 117(3), pages 565-577, September.
    15. Srinivasa, Anand V. & Wilhelm, Wilbert E., 1997. "A procedure for optimizing tactical response in oil spill clean up operations," European Journal of Operational Research, Elsevier, vol. 102(3), pages 554-574, November.
    16. Pourbabai, B. & Ashayeri, J. & Van Wassenhove, L.N., 1992. "Strategic marketing, production, and distribution planning of an integrated manufacturing system," Other publications TiSEM 16c2bacb-2c2b-427e-b429-c, Tilburg University, School of Economics and Management.
    17. Okan Arslan & Ola Jabali & Gilbert Laporte, 2020. "A Flexible, Natural Formulation for the Network Design Problem with Vulnerability Constraints," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 120-134, January.
    18. S. Göttlich & A. Potschka & C. Teuber, 2019. "A partial outer convexification approach to control transmission lines," Computational Optimization and Applications, Springer, vol. 72(2), pages 431-456, March.
    19. Ricardo M. Lima & Ignacio E. Grossmann, 2017. "On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study," Computational Optimization and Applications, Springer, vol. 66(1), pages 1-37, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:jossai:v:8:y:2020:i:3:p:195-223:n:1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.